1 Summary

2 Load packages

suppressPackageStartupMessages({
  library(tidyverse)
  library(mcvis)
  library(corrplot)
  library(mvtnorm)
  library(RColorBrewer)
})
## Warning: replacing previous import 'shiny::renderDataTable' by
## 'DT::renderDataTable' when loading 'mcvis'
theme_set(theme_bw(18) +
            theme(legend.position = "bottom"))

3 Simulation 1: random normal with built linear term

3.1 X1 = X2 + X3

set.seed(1)
p = 10
n = 100

X = matrix(rnorm(n*p), ncol = p)
X[,1] = X[,2] + X[,3] + rnorm(n, 0, 0.1)


ggplot_mcvis(mcvis(X))

corrplot.mixed(cor(X), upper = "square")

3.2 X1 = X2 - X3

X = matrix(rnorm(n*p), ncol = p)
X[,1] = X[,2] - X[,3] + rnorm(n, 0, 0.1)

ggplot_mcvis(mcvis(X))

corrplot.mixed(cor(X), upper = "square")

3.3 X1 = X2 + X3 and X2 = X3 + X4

X = matrix(rnorm(n*p), ncol = p)
X[,1] = X[,2] + X[,3] + rnorm(n, 0, 0.1)
X[,2] = X[,3] + X[,4] + rnorm(n, 0, 0.1)

ggplot_mcvis(mcvis(X))

corrplot.mixed(cor(X), upper = "square")

4 Simulation 2: \(\rho^{|i - j|}\)

4.1 Rho = -0.99

set.seed(1)
rho = -0.99
rows = matrix(rep(c(1:p), p), nrow = p, byrow = F)
cols = t(rows)
XSigma = rho^abs(rows - cols)
X = rmvnorm(n = n, mean = rep(0, p), sigma = XSigma)
mcvis_result = mcvis(X)
ggplot_mcvis(mcvis_result, type = "max")

ggplot_mcvis(mcvis_result, type = "first")

corrplot.mixed(cor(X), upper = "square")

4.2 Rho = 0.99

set.seed(2)
rho = 0.99
rows = matrix(rep(c(1:p), p), nrow = p, byrow = F)
cols = t(rows)
XSigma = rho^abs(rows - cols)
X = rmvnorm(n = n, mean = rep(0, p), sigma = XSigma)
mcvis_result = mcvis(X)
ggplot_mcvis(mcvis_result, type = "max")

ggplot_mcvis(mcvis_result, type = "first")

corrplot.mixed(cor(X), upper = "square")

5 session info

devtools::session_info()
## ─ Session info ──────────────────────────────────────────────────────────
##  setting  value                       
##  version  R version 3.5.1 (2018-07-02)
##  os       macOS High Sierra 10.13.4   
##  system   x86_64, darwin15.6.0        
##  ui       X11                         
##  language (EN)                        
##  collate  en_AU.UTF-8                 
##  ctype    en_AU.UTF-8                 
##  tz       Australia/Sydney            
##  date     2018-12-15                  
## 
## ─ Packages ──────────────────────────────────────────────────────────────
##  package      * version date       lib source        
##  assertthat     0.2.0   2017-04-11 [1] CRAN (R 3.5.0)
##  backports      1.1.2   2017-12-13 [1] CRAN (R 3.5.0)
##  bindr          0.1.1   2018-03-13 [1] CRAN (R 3.5.0)
##  bindrcpp       0.2.2   2018-03-29 [1] CRAN (R 3.5.0)
##  broom          0.5.1   2018-12-05 [1] CRAN (R 3.5.0)
##  callr          3.1.0   2018-12-10 [1] CRAN (R 3.5.0)
##  cellranger     1.1.0   2016-07-27 [1] CRAN (R 3.5.0)
##  cli            1.0.1   2018-09-25 [1] CRAN (R 3.5.0)
##  colorspace     1.3-2   2016-12-14 [1] CRAN (R 3.5.0)
##  corrplot     * 0.84    2017-10-16 [1] CRAN (R 3.5.0)
##  crayon         1.3.4   2017-09-16 [1] CRAN (R 3.5.0)
##  desc           1.2.0   2018-05-01 [1] CRAN (R 3.5.0)
##  devtools       2.0.1   2018-10-26 [1] CRAN (R 3.5.1)
##  digest         0.6.18  2018-10-10 [1] CRAN (R 3.5.0)
##  dplyr        * 0.7.8   2018-11-10 [1] CRAN (R 3.5.0)
##  DT             0.5     2018-11-05 [1] CRAN (R 3.5.0)
##  evaluate       0.12    2018-10-09 [1] CRAN (R 3.5.0)
##  forcats      * 0.3.0   2018-02-19 [1] CRAN (R 3.5.0)
##  foreign        0.8-71  2018-07-20 [1] CRAN (R 3.5.0)
##  fs             1.2.6   2018-08-23 [1] CRAN (R 3.5.0)
##  generics       0.0.2   2018-11-29 [1] CRAN (R 3.5.0)
##  ggplot2      * 3.1.0   2018-10-25 [1] CRAN (R 3.5.0)
##  glue           1.3.0   2018-07-17 [1] CRAN (R 3.5.0)
##  gtable         0.2.0   2016-02-26 [1] CRAN (R 3.5.0)
##  haven          2.0.0   2018-11-22 [1] CRAN (R 3.5.0)
##  hms            0.4.2   2018-03-10 [1] CRAN (R 3.5.0)
##  htmltools      0.3.6   2017-04-28 [1] CRAN (R 3.5.0)
##  htmlwidgets    1.3     2018-09-30 [1] CRAN (R 3.5.0)
##  httpuv         1.4.5   2018-07-19 [1] CRAN (R 3.5.0)
##  httr           1.4.0   2018-12-11 [1] CRAN (R 3.5.1)
##  igraph         1.2.2   2018-07-27 [1] CRAN (R 3.5.0)
##  jsonlite       1.6     2018-12-07 [1] CRAN (R 3.5.0)
##  knitr          1.21    2018-12-10 [1] CRAN (R 3.5.1)
##  labeling       0.3     2014-08-23 [1] CRAN (R 3.5.0)
##  later          0.7.5   2018-09-18 [1] CRAN (R 3.5.0)
##  lattice        0.20-38 2018-11-04 [1] CRAN (R 3.5.0)
##  lazyeval       0.2.1   2017-10-29 [1] CRAN (R 3.5.0)
##  lubridate      1.7.4   2018-04-11 [1] CRAN (R 3.5.0)
##  magrittr       1.5     2014-11-22 [1] CRAN (R 3.5.0)
##  mcvis        * 0.2.5   2018-12-15 [1] local         
##  memoise        1.1.0   2017-04-21 [1] CRAN (R 3.5.0)
##  mime           0.6     2018-10-05 [1] CRAN (R 3.5.0)
##  mnormt         1.5-5   2016-10-15 [1] CRAN (R 3.5.0)
##  modelr         0.1.2   2018-05-11 [1] CRAN (R 3.5.0)
##  munsell        0.5.0   2018-06-12 [1] CRAN (R 3.5.0)
##  mvtnorm      * 1.0-8   2018-05-31 [1] CRAN (R 3.5.0)
##  nlme           3.1-137 2018-04-07 [1] CRAN (R 3.5.1)
##  pillar         1.3.0   2018-07-14 [1] CRAN (R 3.5.0)
##  pkgbuild       1.0.2   2018-10-16 [1] CRAN (R 3.5.0)
##  pkgconfig      2.0.2   2018-08-16 [1] CRAN (R 3.5.0)
##  pkgload        1.0.2   2018-10-29 [1] CRAN (R 3.5.0)
##  plyr           1.8.4   2016-06-08 [1] CRAN (R 3.5.0)
##  prettyunits    1.0.2   2015-07-13 [1] CRAN (R 3.5.0)
##  processx       3.2.1   2018-12-05 [1] CRAN (R 3.5.0)
##  promises       1.0.1   2018-04-13 [1] CRAN (R 3.5.0)
##  ps             1.2.1   2018-11-06 [1] CRAN (R 3.5.0)
##  psych          1.8.10  2018-10-31 [1] CRAN (R 3.5.0)
##  purrr        * 0.2.5   2018-05-29 [1] CRAN (R 3.5.0)
##  R6             2.3.0   2018-10-04 [1] CRAN (R 3.5.1)
##  RColorBrewer * 1.1-2   2014-12-07 [1] CRAN (R 3.5.0)
##  Rcpp           1.0.0   2018-11-07 [1] CRAN (R 3.5.0)
##  readr        * 1.3.0   2018-12-11 [1] CRAN (R 3.5.1)
##  readxl         1.1.0   2018-04-20 [1] CRAN (R 3.5.0)
##  remotes        2.0.2   2018-10-30 [1] CRAN (R 3.5.1)
##  reshape2       1.4.3   2017-12-11 [1] CRAN (R 3.5.0)
##  rlang          0.3.0.1 2018-10-25 [1] CRAN (R 3.5.0)
##  rmarkdown      1.11    2018-12-08 [1] CRAN (R 3.5.0)
##  rprojroot      1.3-2   2018-01-03 [1] CRAN (R 3.5.0)
##  rstudioapi     0.8     2018-10-02 [1] CRAN (R 3.5.0)
##  rvest          0.3.2   2016-06-17 [1] CRAN (R 3.5.0)
##  scales         1.0.0   2018-08-09 [1] CRAN (R 3.5.0)
##  sessioninfo    1.1.1   2018-11-05 [1] CRAN (R 3.5.0)
##  shiny          1.2.0   2018-11-02 [1] CRAN (R 3.5.0)
##  stringi        1.2.4   2018-07-20 [1] CRAN (R 3.5.0)
##  stringr      * 1.3.1   2018-05-10 [1] CRAN (R 3.5.0)
##  testthat       2.0.1   2018-10-13 [1] CRAN (R 3.5.0)
##  tibble       * 1.4.2   2018-01-22 [1] CRAN (R 3.5.0)
##  tidyr        * 0.8.2   2018-10-28 [1] CRAN (R 3.5.0)
##  tidyselect     0.2.5   2018-10-11 [1] CRAN (R 3.5.0)
##  tidyverse    * 1.2.1   2017-11-14 [1] CRAN (R 3.5.0)
##  usethis        1.4.0   2018-08-14 [1] CRAN (R 3.5.0)
##  withr          2.1.2   2018-03-15 [1] CRAN (R 3.5.0)
##  xfun           0.4     2018-10-23 [1] CRAN (R 3.5.1)
##  xml2           1.2.0   2018-01-24 [1] CRAN (R 3.5.0)
##  xtable         1.8-3   2018-08-29 [1] CRAN (R 3.5.0)
##  yaml           2.2.0   2018-07-25 [1] CRAN (R 3.5.0)
## 
## [1] /Library/Frameworks/R.framework/Versions/3.5/Resources/library